Question
Use transformations of the absolute value function,
What transformations are needed in order to obtain the graph of
of
Use the graphing tool to graph the equation.
D.
What transformations are needed in order to obtain the graph of
of
Use the graphing tool to graph the equation.
D.
Ask by Rodriguez Delgado. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The transformations needed are:
- Horizontal shift
- Reflection about the
-axis - Vertical shift
Solution
-
Start with the base function
. -
The function to graph is
. -
The transformation steps are:
-
Horizontal Shift:
The expressionindicates a shift to the right by 4 units. -
Reflection about the
-axis:
The negative sign in front of the absolute value,, reflects the graph across the -axis. -
Vertical Shift:
The termat the end shifts the graph downward by 1 unit.
-
-
The necessary transformations are:
-
A. Horizontal shift -
B. Reflection about the -axis -
F. Vertical shift
-
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Simplify this solution Bonus Knowledge
To transform the absolute value function
First, the expression
- A. Horizontal shift (right by 4)
- B. Reflection about the x-axis
- F. Vertical shift (down by 1)
That’s right for
For graphing, start with the basic shape of
Now grab your graphing tool and see how these transformations change the look of the graph. It’s like taking a standard shape and giving it a makeover! Enjoy graphing!
